US president Barack Obama and his challenger Mitt Romney are storming into the last day of their long presidential contest, mounting a final thrust before Election Day and engaging in the toughest battleground state - Ohio.

The two campaigns' schedules left little doubt where the election would be won or lost: Obama was holding rallies in Wisconsin and Iowa. Romney is in Florida, Virginia and New Hampshire. But the richest prize is Ohio, and both Obama and Romney were rallying their supporters in its capital, Columbus.

Under the US system, the winner is not determined by the nationwide popular vote but in state-by-state contests, making these nine "battleground" states that are neither consistently Republican nor Democratic extremely important in such a tight race.

Romney and Obama are competing to win at least 270 electoral votes. They are apportioned to states based on a mix of population and representation in Congress.

That raises the possibility of a replay of the 2000 election when Republican George W Bush won the presidency with an electoral vote majority, while Democrat Al Gore had a narrow lead in the nationwide popular vote.

Nationwide polls show Obama and Romney locked in one of the closest presidential races in recent American history. But a majority of polls in the battleground states - especially Iowa, Wisconsin and Ohio - show Obama with a slight advantage. No Republican has won the White House without carrying Ohio.

The race was so close that the final national NBC/Wall Street Journal Poll, released on Sunday, showed Obama getting the support of 48% of likely voters, with Romney receiving 47%.

The final national poll from the Pew Research Centre found Obama with a three-point edge over Romney, 48% to 45% among likely voters, an improved showing that indicates the president may have benefited from his response to Superstorm Sandy.

If the election were held now, an Associated Press analysis found that Obama would be all but assured of 249 electoral votes, by carrying 20 states that are solidly Democratic or leaning his way - Iowa, Nevada and Pennsylvania among them - and the District of Columbia.

Romney would lay claim to 206, from probable victories in 24 states that are strong Republican turf or tilt toward the Republicans, including North Carolina. Up for grabs are 83 electoral votes spread across Colorado, Florida, Ohio, New Hampshire, Virginia and Wisconsin. Republicans and Democrats agree Obama seems in slightly better shape in Ohio and Wisconsin, while Romney appears to be performing slightly better or has pulled even in Florida and Virginia.